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Mirrors > Home > ILE Home > Th. List > sb4bor | Unicode version |
Description: Simplified definition of substitution when variables are distinct, expressed via disjunction. (Contributed by Jim Kingdon, 18-Mar-2018.) |
Ref | Expression |
---|---|
sb4bor |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sb4or 1806 | . 2 | |
2 | sb2 1741 | . . . . 5 | |
3 | df-bi 116 | . . . . . 6 | |
4 | 3 | simpri 112 | . . . . 5 |
5 | 2, 4 | mpan2 422 | . . . 4 |
6 | 5 | alimi 1432 | . . 3 |
7 | 6 | orim2i 751 | . 2 |
8 | 1, 7 | ax-mp 5 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wo 698 wal 1330 wsb 1736 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 699 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-4 1488 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 |
This theorem depends on definitions: df-bi 116 df-nf 1438 df-sb 1737 |
This theorem is referenced by: (None) |
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